Polynomial clone reducibility

Polynomial clone reducibility

Polynomial-clone reducibilities are generalizations of the truth-table reducibilities. A polynomial clone is a set of functions over a finite set X that is closed under composition and contains all the constant and projection functions. For a fixed polynomial clone C, a sequence B ∈ X is C-reducible to A ∈ X if there is an algorithm that computes B from A using only effectively selected functio...

On Polynomial-Time Relation Reducibility

We study the notion of polynomial-time relation reducibility among computable equivalence relations. We identify some benchmark equivalence relations and show that the reducibility hierarchy has a rich structure. Specifically, we embed the partial order of all polynomial-time computable sets into the polynomial-time relation reducibility hierarchy between two benchmark equivalence relations Eλ ...

On ~-reducibility versus Polynomial Time Many-one Reducibility*

We prove that each element of a class of f,anctions (denoted by NPCtP), whose graphs can be accepted in nondeterministic polynomial time, can be evaluated in deterministic polynomial time if and only if '/-reducibility is equivalent to polynomial time many-one reducibility. We also modify the proof technique used to obtain part of this result to obtain the stronger result that if every ,/-reduc...

Enumeration Reducibility with Polynomial Time Bounds

We introduce polynomial time enumeration reducibility (≤pe) and we retrace Selman’s analysis of this reducibility and its relationship with non deterministic polynomial time conjunctive reducibility. We discuss the basic properties of the degree structure induced by ≤pe over the computable sets and we show how to construct meets and joins. We are thus able to prove that this degree structure is...

Random-self-reducibility in the Polynomial Hierarchy